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Sech




Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving coth > Involving coth(c z)(a+b sech2(c z))beta





http://functions.wolfram.com/01.24.21.0476.01









  


  








Input Form





Integrate[Coth[c z]/Sqrt[a + b Sech[c z]^2], z] == -(Sqrt[a + 2 b + a Cosh[2 c z]] (Sqrt[a] ArcTanh[(Sqrt[2 a + 2 b] Cosh[c z])/ Sqrt[a + 2 b + a Cosh[2 c z]]] - Sqrt[a + b] Log[Sqrt[2] Sqrt[a] Cosh[c z] + Sqrt[a + 2 b + a Cosh[2 c z]]]) Sech[c z])/(Sqrt[a] Sqrt[2 a + 2 b] c Sqrt[a + b Sech[c z]^2])








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Sech", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List["a", "+", RowBox[List["2", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["a"], " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox[RowBox[List["a", "+", RowBox[List["2", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["a", "+", "b"]]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox["a"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["2", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]]]], ")"]], " ", RowBox[List["Sech", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[SqrtBox["a"], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", "c", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Sech", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2002-12-18